Non-holomorphic Cuspidal Automorphic Forms of GSp(4;A) and the Hodge Structure of Siegel Threefolds
Bibliographic record
Abstract
Let V( ) denote a local system of weight on X = A2;n(C), where X is the moduli space\nof principle polarized abelian varieties of genus 2 over C with xed n-level structure. The\ninner cohomology of X with coe cients in V( ), H3\n! (X;V( )), has a Hodge ltration\nof weight 3. Each term of this Hodge ltration can be presented as space of cuspidal\nautomorphic representations of genus 2. We consider the purely non-holomorphic part\nof H3\n! (X;V( )) denoted by H3\nEnds(X;V( )).\nFirst of all we show that there is a non-zero subspace of H3\nEnds(X;V( )) denoted by\nV (K), where K is an open compact subgroup of GSp(4;A), such that elements of\nV (K) are obtained by the global theta lifting of cuspidal automorphic representations\nof GL(2) GL(2)=Gm. This means that there is a non-zero part of H3\nEnds(X;V( )) which\nis endoscopic.\nSecondly, we consider the local theta correspondence and nd an explicit answer for the\nlevel of lifted cuspidal automorphic representations to GSp(4; F) over a non-archimedean\nlocal eld F. Therefore, we can present an explicit way for nding a basis for V (K) for\na xed level structure K.\nii\nThere is a part of the Hodge structure that only contributes in H(3;0)\n! (X;V( )) H(0;3)\n! (X;V( )).\nThis part is endoscopic and coming from the Yoshida lift from O(4).\nFinally, in the case X = A2, if eendo(A2;V( )) denotes the motive corresponded to the\nstrict endoscopic part (the part that contributes only in non-holomorphic terms of the\nHodge ltration), then we have\neendo(A2;V( )) = s 1+ 2+4S[ 1 2 + 2]L 2+1; (1)\nwhere = ( 1; 2) and is far from walls. Here S[k] denotes the motive corresponded\nto Sk, the space of cuspidal automorphic forms of weight k and trivial level, and sk =\ndim(Sk).\nii
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".